On cosmological constants from α′-corrections

  • Friðrik Freyr Gautason
  • Daniel Junghans
  • Marco Zagermann


We examine to what extent perturbative α′-corrections can generate a small cosmological constant in warped string compactifications. Focusing on the heterotic string at lowest order in the string loop expansion, we show that, for a maximally symmetric spacetime, the α′-corrected 4D scalar potential has no effect on the cosmological constant. The only relevant terms are instead higher order products of 4D Riemann tensors, which, however, are found to vanish in the usual perturbative regime of the α′-expansion. The heterotic string therefore only allows for 4D Minkowski vacua to all orders in α′, unless one also introduces string loop and/or nonperturbative corrections or allows for curvatures or field strengths that are large in string units. In particular, we find that perturbative α′-effects cannot induce weakly curved AdS4 solutions.


Superstrings and Heterotic Strings dS vacua in string theory Superstring Vacua 


  1. [1]
    V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and alpha-prime corrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].MathSciNetADSGoogle Scholar
  4. [4]
    L. Anguelova and C. Quigley, Quantum corrections to heterotic moduli potentials, JHEP 02 (2011) 113 [arXiv:1007.5047] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    L. Anguelova, C. Quigley and S. Sethi, The leading quantum corrections to stringy Kähler potentials, JHEP 10 (2010) 065 [arXiv:1007.4793] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    M. Dine and N. Seiberg, Couplings and scales in superstring models, Phys. Rev. Lett. 55 (1985) 366 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    M. Dine and N. Seiberg, Is the superstring weakly coupled?, Phys. Lett. B 162 (1985) 299 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    S.S. Haque, G. Shiu, B. Underwood and T. Van Riet, Minimal simple de Sitter solutions, Phys. Rev. D 79 (2009) 086005 [arXiv:0810.5328] [INSPIRE].ADSGoogle Scholar
  10. [10]
    C. Caviezel et al., On the cosmology of type IIA compactifications on SU(3)-structure manifolds, JHEP 04 (2009) 010 [arXiv:0812.3551] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    R. Flauger, S. Paban, D. Robbins and T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes, Phys. Rev. D 79 (2009) 086011 [arXiv:0812.3886] [INSPIRE].ADSGoogle Scholar
  12. [12]
    M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary constraints on type IIA string theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    E. Silverstein, Simple de Sitter solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [INSPIRE].MathSciNetADSGoogle Scholar
  14. [14]
    U.H. Danielsson, S.S. Haque, G. Shiu and T. Van Riet, Towards classical de Sitter solutions in string theory, JHEP 09 (2009) 114 [arXiv:0907.2041] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    B. de Carlos, A. Guarino and J.M. Moreno, Flux moduli stabilisation, supergravity algebras and no-go theorems, JHEP 01 (2010) 012 [arXiv:0907.5580] [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    T. Wrase and M. Zagermann, On classical de Sitter vacua in string theory, Fortsch. Phys. 58 (2010) 906 [arXiv:1003.0029] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    O. Lechtenfeld, C. Nolle and A.D. Popov, Heterotic compactifications on nearly Kähler manifolds, JHEP 09 (2010) 074 [arXiv:1007.0236] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    A. Chatzistavrakidis, O. Lechtenfeld and A.D. Popov, Nearly Káhler heterotic compactifications with fermion condensates, JHEP 04 (2012) 114 [arXiv:1202.1278] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    S.R. Green, E.J. Martinec, C. Quigley and S. Sethi, Constraints on string cosmology, Class. Quant. Grav. 29 (2012) 075006 [arXiv:1110.0545] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    J. Held, D. Lüst, F. Marchesano and L. Martucci, DWSB in heterotic flux compactifications, JHEP 06 (2010) 090 [arXiv:1004.0867] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    B.A. Campbell, M.J. Duncan, N. Kaloper and K.A. Olive, Gravitational dynamics with Lorentz Chern-Simons terms, Nucl. Phys. B 351 (1991) 778 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  22. [22]
    B. Underwood, A breathing mode for warped compactifications, Class. Quant. Grav. 28 (2011) 195013 [arXiv:1009.4200] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    J. Derendinger, L.E. Ibáñez and H.P. Nilles, On the low-energy D = 4, N = 1 supergravity theory extracted from the D = 10, N = 1 superstring, Phys. Lett. B 155 (1985) 65 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    M. Dine, R. Rohm, N. Seiberg and E. Witten, Gluino condensation in superstring models, Phys. Lett. B 156 (1985) 55 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].MathSciNetADSGoogle Scholar
  26. [26]
    H. Kunitomo and M. Ohta, Supersymmetric AdS 3 solutions in heterotic supergravity, Prog. Theor. Phys. 122 (2009) 631 [arXiv:0902.0655] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    M.R. Douglas and R. Kallosh, Compactification on negatively curved manifolds, JHEP 06 (2010) 004 [arXiv:1001.4008] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    J. Blaback et al., Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
  30. [30]
    R.M. Wald, General Relativity, University of Chicago Press, Chicago U.S.A. (1984).CrossRefzbMATHGoogle Scholar
  31. [31]
    A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    B. de Wit, D. Smit and N. Hari Dass, Residual supersymmetry of compactified D = 10 supergravity, Nucl. Phys. B 283 (1987) 165 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Friðrik Freyr Gautason
    • 1
  • Daniel Junghans
    • 1
  • Marco Zagermann
    • 1
  1. 1.Institut für Theoretische Physik & Center for Quantum Engineering and Spacetime ResearchLeibniz Universität HannoverHannoverGermany

Personalised recommendations